where is cat id in database?

hello!
i’m using the following code to retrive titles and ids of posts from my database.

$ids = $wpdb->get_col("SELECT id FROM $wpdb->posts WHERE post_type = 'post' AND post_status = 'publish'");
$titles= $wpdb->get_col("SELECT post_title FROM $wpdb->posts WHERE post_type = 'post' AND post_status = 'publish'");

i want make it to select $ids and $titles for only one category, but i could’t find specific field.
So can anyone point me where(which table and filed name)is cat id for post?